How do you factor the trinomial #16x^2-40xy+25y^2#?

Question

Savannah Anderson · Accepted Answer

3(4x - 5y)^2#

#(4x - 5y)^2 = 16x^2 - 40xy + 25y^2#

Jameson Allen · Answer

undefined To factor the trinomial $16x^2 - 40xy + 25y^2$, you can use the following steps:

1. Identify whether the trinomial can be factored further by checking if it fits the form $ax^2 + bx + c$.

2. If it fits the form, determine the factors of the first and last terms, which are $16x^2$ and $25y^2$, respectively.

3. Find two numbers that multiply to $16 \times 25 = 400$ and add up to the middle coefficient $40$.

4. The numbers are $20$ and $20$. Rewrite the middle term $40xy$ using these numbers, which gives $16x^2 - 20xy - 20xy + 25y^2$.

5. Group the terms in pairs: $16x^2 - 20xy$ and $-20xy + 25y^2$.

6. Factor out the greatest common factor from each pair. The GCF of the first pair is $4x$, and the GCF of the second pair is $-5y$.

7. After factoring, you'll have $4x(4x - 5y) - 5y(4x - 5y)$.

8. Notice that both terms have the common factor $(4x - 5y)$. Factor this out, and you'll get $(4x - 5y)(4x - 5y)$.

So, the factored form of $16x^2 - 40xy + 25y^2$ is $(4x - 5y)^2$.